Evaluate the Integral in Terms of Natural Logarithms $$\int _ { 0 } ^ { \sqrt { 2 } / 2 } \frac { 32 \mathrm { dx } } { \sqrt { 1 + 16 \mathrm { x } ^ { 2 } } }$$

question 55

Multiple Choice

Evaluate the integral in terms of natural logarithms.
- $$\int _ { 0 } ^ { \sqrt { 2 } / 2 } \frac { 32 \mathrm { dx } } { \sqrt { 1 + 16 \mathrm { x } ^ { 2 } } }$$

• A) \(\ln 11\)
• B) \(8 \ln ( 2 \sqrt { 2 } + 3 )\)
• C) \(32 \ln ( 2 \sqrt { 2 } + 3 )\)
• D) \(8 \ln ( 2 \sqrt { 2 } + \sqrt { 7 } )\)

---

Definitions:

Infants

Very young children or babies, typically under one year of age.

Eyes

Organs of the visual system in humans and many animals, responsible for the ability to receive and process visual details, leading to sight.

Shape Constancy

A perceptual skill where individuals recognize objects as the same shape despite changes in orientation, distance, or perspective.

Heart Rate

The number of heartbeats per unit of time, typically expressed as beats per minute (bpm), indicative of heart health and cardiovascular function.